Question
Roni's parents are planning a vacation. They found a cabin to rent for $75 a day with no deposit.
y = 75x
They also found a hotel that was $45 a day, with a $60 deposit.
y = 45x + 60
The costs for the two vacation rentals are shown on the graph below.
How many nights can they stay at the hotel or the cabin and pay the same amount of money?
y = 75x
They also found a hotel that was $45 a day, with a $60 deposit.
y = 45x + 60
The costs for the two vacation rentals are shown on the graph below.
How many nights can they stay at the hotel or the cabin and pay the same amount of money?
Answers
Answered by
GPT-4o mini
To find out how many nights Roni's parents can stay at the hotel or the cabin for the same cost, we need to set the two cost equations equal to each other and solve for \( x \), where \( x \) represents the number of nights stayed.
The equation for the cabin is:
\[
y = 75x
\]
The equation for the hotel is:
\[
y = 45x + 60
\]
Setting the two equations equal to each other gives:
\[
75x = 45x + 60
\]
Now, we can solve for \( x \):
1. Subtract \( 45x \) from both sides:
\[
75x - 45x = 60
\]
\[
30x = 60
\]
2. Now, divide by 30:
\[
x = \frac{60}{30} = 2
\]
Thus, Roni's parents can stay for **2 nights** at both the hotel and the cabin before the costs are equal.
The equation for the cabin is:
\[
y = 75x
\]
The equation for the hotel is:
\[
y = 45x + 60
\]
Setting the two equations equal to each other gives:
\[
75x = 45x + 60
\]
Now, we can solve for \( x \):
1. Subtract \( 45x \) from both sides:
\[
75x - 45x = 60
\]
\[
30x = 60
\]
2. Now, divide by 30:
\[
x = \frac{60}{30} = 2
\]
Thus, Roni's parents can stay for **2 nights** at both the hotel and the cabin before the costs are equal.